Error analysis for Galerkin-BDF discretizations of DAEs with elliptic operator constraints

Abstract

We are interested in a convergent numerical discretization scheme for nonlinear differential algebraic equations (DAEs) coupled with elliptic constraints. The dynamics of flow networks (for example circuits) can often be described by a DAE. However, this is only the case if all network element models are lumped models. If spatial effects cannot be neglected, distributed element models have to be included. In this paper, we address the case of elliptic models for distributed network elements. Under some monotonicity and Lipschitz assumptions for the system functions, we present an error analysis for discretizations of DAEs coupled with elliptic constraints based on a Galerkin approach for the distributed model part combined with the BDF method as time discretization of the full system.